{"paper":{"title":"Generic-case complexity of Whitehead's algorithm, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich","submitted_at":"2019-03-17T07:42:03Z","abstract_excerpt":"In \\cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that \"generic\" elements of $F_N$ are \"strictly minimal\" in their $Out(F_N)$-orbits. Here we generalize these results, with appropriate modifications, to a much wider class of random processes generating elements of $F_N$. We introduce the notion of a ''$(M,\\lambda, \\epsilon)$-minimal\" conjugacy class $[w]$ in $F_N$, where $M\\ge 1, \\lambda>1$ and $0<\\epsilon<1$. Roughly, being $(M,\\lambda, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07040","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}